<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Galton's data on the heights of parents and their children</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link rel="stylesheet" type="text/css" href="R.css" />
</head><body>

<table width="100%" summary="page for Galton"><tr><td>Galton</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>
Galton's data on the heights of parents and their children
</h2>

<h3>Description</h3>

<p>Galton (1886) presented these data in a table, showing a cross-tabulation of
928 adult children born to 205 fathers and mothers, by their height and
their mid-parent's height.
He visually smoothed the bivariate frequency distribution and showed that the
contours formed concentric and similar ellipses, thus setting the stage for
correlation, regression and the bivariate normal distribution.
</p>


<h3>Usage</h3>

<pre>data(Galton)</pre>


<h3>Format</h3>

<p>A data frame with 928 observations on the following 2 variables.
</p>

<dl>
<dt><code>parent</code></dt><dd><p>a numeric vector: height of the mid-parent (average of father and mother)</p>
</dd>
<dt><code>child</code></dt><dd><p>a numeric vector: height of the child</p>
</dd>
</dl>



<h3>Details</h3>

<p>The data are recorded in class intervals of width 1.0 in. He used non-integer
values for the center of each class interval because of the strong bias toward
integral inches.
</p>
<p>All of the heights of female children were multiplied by 1.08  before tablulation
to compensate for sex differences.  See Hanley (2004) for a reanalysis of
Galton's raw data questioning whether this was appropriate.
</p>


<h3>Source</h3>

<p>Galton, F. (1886). Regression Towards Mediocrity in Hereditary Stature
<em>Journal of the Anthropological Institute</em>, 15, 246-263
</p>


<h3>References</h3>

<p>Friendly, M. &amp; Denis, D. (2005). The early origins and development of the scatterplot. 
<em>Journal of the History of the Behavioral Sciences</em>, 
41, 103-130.
</p>
<p>Galton, F. (1869). <em>Hereditary Genius: An Inquiry into its Laws and Consequences</em>.
London: Macmillan.
</p>
<p>Hanley, J. A. (2004). &quot;Transmuting&quot; Women into Men: Galton's Family Data on Human Stature.
<em>The American Statistician</em>, 58, 237-243.
See: <a href="http://www.medicine.mcgill.ca/epidemiology/hanley/galton/">http://www.medicine.mcgill.ca/epidemiology/hanley/galton/</a> for source materials.
</p>
<p>Stigler, S. M. (1986). 
<em>The History of Statistics: The Measurement of Uncertainty before 1900</em>.
Cambridge, MA: Harvard University Press, Table 8.1
</p>
<p>Wachsmuth, A. W., Wilkinson L., Dallal G. E. (2003). 
Galton's bend: A previously undiscovered nonlinearity in Galton's family stature regression data. 
<em>The American Statistician</em>, 57, 190-192. 
<a href="http://www.cs.uic.edu/~wilkinson/Publications/galton.pdf">http://www.cs.uic.edu/~wilkinson/Publications/galton.pdf</a>
</p>


<h3>See Also</h3>

<p><code>link{GaltonFamilies}</code>,
<code>PearsonLee</code>,
<code>galton</code>
</p>


<h3>Examples</h3>

<pre>

data(Galton)

###########################################################################
# sunflower plot with regression line and data ellipses and lowess smooth
###########################################################################

with(Galton, 
	{
	sunflowerplot(parent,child, xlim=c(62,74), ylim=c(62,74))
	reg &lt;- lm(child ~ parent)
	abline(reg)
	lines(lowess(parent, child), col="blue", lwd=2)
	if(require(car)) {
	dataEllipse(parent,child, xlim=c(62,74), ylim=c(62,74), plot.points=FALSE)
		}
  })

</pre>


</body></html>
